Question

What is the cost of one pound of nitrogen from a fertilizer containing 33.5% sodium nitrate by weight and costing $9.00 per 100 lb?

Options:
A) $2.69
B) $3.02
C) $4.07
D) $5.06

Answer 1

To find the cost of one pound of nitrogen in a fertilizer containing 33.5% sodium nitrate, calculate the total nitrogen content and then the price per pound. None of the given options match the calculated value of approximately $1.19 per pound of nitrogen.

Step-by-step explanation:

The question is asking for the cost of one pound of nitrogen from a batch of fertilizer containing 33.5% sodium nitrate by weight and costing $9.00 per 100 lb. To find the answer, we first calculate the total weight of sodium nitrate in the 100 lb of fertilizer, which is 33.5% of 100 lb. Then, we determine the weight of nitrogen in the sodium nitrate using its molecular weight composition. Sodium nitrate (NaNO3) contains roughly 22.6% nitrogen by weight. After calculating the total weight of nitrogen, we find the cost per pound of the nitrogen within the fertilizer.

1. Calculate the weight of sodium nitrate: 100 lb * 33.5% = 33.5 lb of NaNO3.
2. Calculate the weight of nitrogen in sodium nitrate: 33.5 lb * 22.6% ≈ 7.57 lb of N.
3. Calculate the cost per pound of nitrogen: $9.00 for 100 lb / 7.57 lb of N ≈ $1.19 per pound of N (which does not match any of the given options).

It is important to note that none of the provided options (A) $2.69, (B) $3.02, (C) $4.07, or (D) $5.06 matches the calculated value. Therefore, either there is an issue with the options provided or further clarification is required on the question.